curve #3280

y² = x³ − 11x + 890

a-invariants: [0, 0, 0, -11, 890]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/4ℤ
conductor (N): 272
discriminant (Δ): -342102016
Faltings height: 0.3165
naive height: 27.1056
primes of bad reduction: 2, 17
regulator: 2.036297434690738342122104749035702383459
submitted by: David Renshaw
submitted at: 2026-09-26 20:50:47 UTC
last updated: 2026-09-26 20:50:47 UTC

Witness: 1 independent point log in to add more points →

(-1, 30)

Commentary

Cremona 272b4 = LMFDB 272.b4: https://www.lmfdb.org/EllipticCurve/Q/272/b/4 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 272, minimal discriminant -342102016, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:50:47 UTC · history